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The Ski Rental Problem
- comrade1234 1y agoDo like many people in Switzerland and just rent skis for the full season. That way you get a new pair every year. You should own your own custom-fitted boots though.
- amelius 1y agoObviously, the skiing is not what the article is about, really.
- taminka 1y agoit's cheaper to just buy your own pair at that point, not to mention that those skis are usually beat up, and mostly beginner/intermediate level...
- tempay 1y agoIn Switzerland it varies. Many places will also offer expert hire where you get brand-new skis and at the end of the season you can choose to buy them for cost.
- Loic 1y agoFYI, the rental skis, even if they look the same as the same skis you could buy retail are not the same. They have bigger edges and a dicker base. The bindings are not the same. This is because they are built to go through the machine after each rental. Good retails skis have less "robust" but faster, thinner base, they would be dead after 3 months of rental. Source: I spend way too many hours each season in a ski shop taking care of a mix of rental and competitive hardware.
- rkomorn 1y agoI always suspected my rental skis had dicker bases! (Sorry for typo-sniping for cheap laughs.)
- Loic 1y agoFrench living in Germany, sometimes I am mixing up things. What is interesting is that the Swiss person (probably German speaking) did not notice. Thank you for allowing to laugh after the fact :-D
- rkomorn 1y agoThis is a double bonus thread for me. I did not know (or remember from high school German 30 years ago...) that dicker meant thicker. :D
- bee_rider 1y agoI’ve rented skis in the US for a weekend out skiing, and of course they are usually pretty beat up (to be expected), and I don’t expect any amazing performance (wasted on me anyway). But, they are taking about something that seems a bit different, renting skis for a whole season. Almost seems more like leasing a car vs renting one?
- poulsbohemian 1y ago>This is because they are built to go through the machine after each rental What machine are you referring to here? It sounds like you are referring to some kind of waxing / edge sharpening / cleaning device, which would be extreme luxury compared to the rental shop at my local hill where they intake the rentals for the day and dump them back into a bucket for the next skier.
- bee_rider 1y agoRenting for a whole season seems pretty different from renting for a weekend or whatever. I wouldn’t be surprised if it was the more expensive option than buying—but you get brand new skis every year. Maybe for us in the US, this is more equivalent to buying every year and then reselling? Haha.
- bee_rider 1y agoWhen people in the US think of rental skis, we think of weekend rentals that are usually not very specialized and pretty beat up. What you describe here sounds more like leasing a car vs renting one—technically a lease is a rental, but practically it is a bit closer to owning the thing.
- einarfd 1y agoAre you sure that there aren't multiple tiers of rental skies in resorts in the USA? I have friends in the rental business in Norway, and they rent out skies from the kind of beginner friendly skies that would fit your description. To top of the line Stockli and Van Deer kit. I think they keep all of their gear in at least decent shape, with the top gear kept in the best shape, as it makes the most difference for those customers. Btw. haven't rented much in the Alps. But my impression is that you can rent gear for all ability levels there aswell, and that that gear is kept in good shape.
- bee_rider 1y agoI’m not sure there aren’t, in fact I bet there are! I’m just talking about the typical case that I think most people think of.
- ghaff 1y agoWhen I was downhill skiing, there were typically regular rentals and performance rentals. I'd usually bring my own boots but, if traveling by air, usually rent the skis.
- rr808 1y agoHere in NY region seasonal rentals are pretty common too. Esp for kids who will upsize every year or two.
- 1659447091 1y ago> You should own your own custom-fitted boots though I would preach this with snowboard boots (+ helmet), made travel easier as well when you live nowhere near snow. Trying to take up skiing now and have no idea why I didn't think to do this with ski boots. Would probably help, a lot. As for rentals it's easy to avoid beat-up janky gear. Have to go places just outside the ski town areas. Usually have to find a shop outside the resort for snowboards if you bring your own boots anyway, but easier to find better gear options. I remember getting a new (or basically new) K2 board from a general sports store in Reno, same for getting rentals in Queenstown or Denver or Vancouver before hopping on a bus. Shops outside the resorts tend to have reasonably priced demo rentals, newer high end gear they are hoping you buy afterwards. Far better equipment that is nicely tuned than anything the resorts offer. Not paying the oversize/ski baggage fee and lugging that gear around the whole trip while having quality rentals available levels the rent vs buy equation -- if buying a season lift pass makes sense so does buying your own gear, otherwise it's more hassle than it needs to be, imo.
- tantalor 1y agoIs this related to the secretary problem?
- polivier 1y agoKind of, in the sense that you need to make a decision about something mid-way when there is still some unknown information ahead of you.
- cwmoore 1y agoMaybe the relatable concept is just a stepladder to the general ongoing scenario, eg. modeling all consumers from a retailer’s perspective. Otherwise, the continuous to discrete assumption reads as a hand-wavy fiat. Could someone who groks this math tell me why not buy the skis once you’ve paid half their price on rentals?
- rzzzt 1y agoWhy stop there and instead buy when 33% of the equipment cost is spent on renting?
- pfedak 1y agoAnother aspect of the solution that makes it rather abstract is it effectively assumes we know nothing about the distribution of the number of days. Paying at 1/2 will be optimal if it ends before you buy, very bad (3x optimal) if it ends right after you buy, and slightly better than the solution in the post if it lasts at least twice that long (1.5x optimal vs e/(e-1)). The metric in the post is just the worst of those ratios. Assuming the unproven statement in the post (that the solution which is a constant factor worse than optimal is best), any solution of the form you suggest is going to have similar tradeoffs. If we had a distribution, we could choose.
- lisbbb 1y agoOh man, I had no idea that the decision of whether to rent or buy skis required calculus to solve. I just figured that if you ski more than say, 3 times a season, it's probably better to own your own gear for reasons unrelated to the entry cost, but more to do with comfort, tuning, quality, and so on. Anyone who has rented skis knows that the rental fleets are trashed.
- phillipcarter 1y agoYeah it's a fun problem but not really related to reality. Some important factors like: proximity to different ski resorts, travel plans, whether to rent demo skis or not, quality of rental skis, skiing proficiency and desire to grow, and many more all factor into the decision. Suffice to say, it's not much of an optimization problem if you're set on skiing every year.
- coderatlarge 1y agoalso ski prices probably vary throughout the season
- Noumenon72 1y agoI have rented skis perhaps 70 times in my life and I have nothing bad to say about them. Maybe a broken buckle once or twice.
- nothercastle 1y agoNothing wrong with the rental skis but time ain’t free
- geokon 1y agoits been a while since i was serious about skiing. but my impression was that when it comes to comfort, the most important factor was getting good boots Renting skiis is okay. lets you try out a lot of different kinds. They all ride different
- bmacho 1y ago
- armanboyaci 1y agoWhat happens if you have a prior knowledge for $k$ as a probability distribution?
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- massung 1y agoThis feels very similar to the “radio” or “restaurant” problem: You’re driving down the street trying to decide which restaurant to stop at (or scanning through the radio trying to decide which song to stop on). If you stop at the first, there’s a good chance something better is ahead. But if you wait too long then you risk getting stuck with something you don’t really like (the problem assumes you can’t go back). If I remember correctly, mathematically you skip the first 1/3, but keep track of your “best”. Then stop at the next option that’s >= than your current best or maybe the next thing you like. With respect to skis, I have the same issue every year with a ride on lawn mower. Do I just pay someone weekly or buy one outright and do it myself? In this case I loathe mowing, so I don’t mind paying. But with skis it’s a question of just how much I’ll ski after this stretch, regardless of whether or not this stretch is 1 or 20 days. Because there are additional costs (and benefits) to ownership beyond the initial purchase.
- pmalynin 1y agoI think it was 1/e but close enough (37%) https://en.wikipedia.org/wiki/Secretary_problem#1.2Fe-law_of_best_choice https://en.wikipedia.org/wiki/Secretary_problem#1.2Fe-law_of...
- eterm 1y agoIt's known to wikipedia as the "Secretary Problem": https://en.wikipedia.org/wiki/Secretary_problem https://en.wikipedia.org/wiki/Secretary_problem The optimum is actually based on 1/e rather than 1/3 but 1/3 is a good enough practical approximation.
- svat 1y agoIn the secretary problem, you're trying to maximize the probability of selecting the absolutely best candidate. In other words you assume that you “win” if you select the best candidate and “lose” otherwise (even if you end up picking the second best who is almost as good!), and you're trying to maximize the probability of winning. (The optimal solution says you can win with probability 1/e ≈ 37%, meaning that ≈63% of the time you lose!) This has always seemed the most unsatisfying assumption in the problem to me, with application to no real-life case that I can think of. The Wikipedia article has some stuff on relaxing this assumption, in its section titled “Cardinal payoff variant” (it seems that the optimal at least under one set of assumptions is √n rather than n/e, though those assumptions also seem unrealistic): https://en.wikipedia.org/w/index.php?title=Secretary_problem&oldid=1302476617#Cardinal_payoff_variant https://en.wikipedia.org/w/index.php?title=Secretary_problem...
- thrawa8387336 1y agoRent until you know what you want to buy. Done
- xandrius 1y agoBuy second-hand and worst case resell. Best of both worlds.
- RealStickman_ 1y agoIn many stores you can ask for "test skis". These would have been used for a few weeks as rentals and you usually get a significant discount from the normal retail price
- robocat 1y agoYou also get 'test bindings' that both toe and heel can be shifted forward/back to adjust to fit most boots. Disadvantage: weight. Advantage: adjustable. On normal bindings the toe is often screwed in at one location to fit your boots and cannot be shifted later.
- ip26 1y agoThe second-hand market is a bit of a mess unless you're comparing among the most popular skis. The depreciation is also brutally steep. You can avoid the depreciation issue with old skis, but that comes with other problems.
- SkyPuncher 1y agoSki swaps are a great place for second hand or almost second hand. I’ve been to many where the local ski shops dump their old inventory. You get pretty much pristine gear for a fraction of the price.
- andai 1y agoThis kind of blew my mind when I realized that if you buy second hand and resell, you can own a product (often for years) for net zero dollars. I was also delighted when I realized that instead of going through the hassle and cost of moving everything across the country, I could just sell it and buy roughly the same thing in the new place... again for net zero dollars! Teleportation!
- matchagaucho 1y agoEvery time my wife brings up the skis collecting dust in our garage, I’m reminded of the S.K.I. model — Storage Kills Investment.
- Cerium 1y agoAt least yours are in the garage. I have a friend who spent years storing a couple of hundred dollars of outdoor gear in a rental storage locker costing $50 per month.
- SteveNuts 1y agoI have relatives that have spent $60/mo for a storage unit for 12 years for some furniture they "might want to use some day if they buy a new house". Even pointing out that the furniture will likely look extremely dated by now and they've spent almost $10k so far doesn't seem to click at all.
- Daviey 1y agoBut now it's a sunk cost, might as well keep it going, right?
- SteveNuts 1y agoExactly! Why cut your losses now when it’ll surely pay off in 10 more years
- ghaff 1y agoBasically, don't rent a storage locker unless you have a fairly specific exit plan. There may be exceptions like I have no intention of moving out of a condo/apartment but I do sports that require fairly large equipment. But it's a good rule-of-thumb.
- rossjudson 1y agoYeah, that's what you think the storage locker is for.
- JohnKemeny 1y agoHere's a different version of the problem. It takes 10 minutes to walk home from the bus central. The bus is late but should be here any minute now. The bus takes one minute. Do you wait or walk?
- xandrius 1y agoAlways decide to walk, especially for just 10 minutes. Good for health, mental wellbeing and it's just easy. If the question was 1h+ then maybe the answer would be different.
- JohnKemeny 1y agoIt's a computational problem, I thought (mistakenly) that the HN crowd would understand.
- speed_spread 1y agoYour explanation was too good, people go straight for the answer to your example. There might be a bit of cheekiness too!
- mikestew 1y ago10 minutes? Always walk. Walking then becomes a known quantity, unlike your bus, and your health will benefit. And, yeesh, it’s only a ten minute walk.
- JohnKemeny 1y agoIt's a problem from computer science, not Dr Oz. You want to optimize for when you get home, not for your health or environment.
- porridgeraisin 1y agoDon't you need to know the inter arrival time to solve this? I think the point is that it's a memory less distribution so you're expected to wait for the same time regardless of how long you've already waited.
- Tycho 1y agoSkiing is incredibly fun but I wonder if it should be put in the same category as cycling (on roads): too dangerous to be sane.
- bix6 1y agoIt seems many fun things are dangerous :)
- _kyran 1y agoThere’s a large spectrum between skiing on an uncrowded slope alone, a crowded beginner trail, hucking cliffs and backcountry in avy prone terrain. I don’t think the risk profile can be all lumped together. Much in the same way that cycling on the road has a different risk profile to on a bike path vs downhill or freeride mountain biking.
- nothercastle 1y agoMost people get hurt because they try to learn in an uncontrolled fashion and overestimate their skill.
- mritterhoff 1y agoCycling on roads could be safer, but in the US at least, we're numb to car-caused deaths.
- rkagerer 1y agoOr just buy the skis and sell them on the used market when you no longer need them. Stop paying the SaaS tax.
- leifmetcalf 1y agoWhy do we have that E[max_k alg(k)/opt(k)] is equal to max_k E[alg(k)]/opt(k) ?
- poulsbohemian 1y agoThis is kind of an interesting problem, but it overlooks another variable, at least in the case of skis - it's not just how many days I'm going to use them this year, but also for the next few years. Yes, there are people who buy new skis regularly, but more commonly the person that makes the buy vs rent decision decides that over the next multiple seasons they intend to ski enough to justify the buy decision. This is especially true if you are buying new skis rather than say, rental skis at the end of the season (think kinda like buying a used car that has been depreciated, you can buy used skis that still have a lot of miles...). So my point is simply that the real world problem is actually even more interesting than this hypothetical.